In general, a conventional chair has two chair armrests. In order to provide more comfort, some conventional chair armrests are designed to be movable in a front-rear direction and a left-right direction for adjusting the chair armrests forward, rearward, rightward or leftward. A conventional armrest whose position is adjustable along a horizontal surface is disclosed in Taiwanese Patent No. I353822, and includes a bottom seat, a cap body, a fixing device, and an adjusting member disposed between the bottom seat and the cap body. The fixing device includes a base plate having a plurality of first tooth portions, a fixing plate having two rows of second tooth portions, and two gears disposed at two opposite sides of the fixing plate and respectively mesh with the second tooth portions of the fixing plate. The adjusting member has two racks, one of the racks having a plurality of first rack teeth capable of meshing with the first tooth portions of the base plate, and the other one of the racks having a plurality of second rack teeth capable of meshing with the gears. When the first rack teeth mesh with the first tooth portions of the base plate, and when the second rack teeth mesh with the gears, the bottom seat and the cap body are locked against movement. When the first rack teeth are away from the first tooth portions of the base plate, and when the second rack teeth are away from the gears, a user may grip the bottom seat and the cap body with his/her hand to move the same in the front-rear direction and the left-right direction to adjust the position of the armrest.